| Charles Hutton - Science - 1815
...form a right-angled triangle CDE or CDH, of which the radius CD is the hypothenuse ; and therefore **the square of the radius is equal to the sum of the** squares of the sine and cosine of any arc, that is, CD* = CE* -*- ED* or = сн1 -i- DH*. It is evident... | |
| Abraham Crocker, Richard Farley - 1841
...sura of the squares of the chord of an arc, and of the chord of its supplement to a semi-circle. 2. **The square of the radius is equal to the sum of the** squares of the sine and co-sine. 3. The sum of the co-sine and versed-sine is equal to the radius.... | |
| George Clinton Whitlock - Mathematics - 1848 - 324 pages
...tan(90° — a) ; &c. (303) seca = cosec(90° — a), coseca = sec(90° — a) ; &c. (304) PROPOSITION I. **The sum of the squares of the sine and cosine of an** arc (305) is equal to the square of the radius, or to unity, when the radius is taken for the unit... | |
| Alexander Ingram - 1851
...the sine of half that arc : Thus BG = ^BL. 2. In the right-angled triangle CGB, CB2 = CG2 + GB2, or **the square of the radius is equal to the sum of the** squares of the sine and cosine of any arc; hence sin. = /J(R3 — cos.2), cos. = V(R2 — sin.2), or... | |
| Edward Butler (A.M.) - 1862
...cos A' cos A' The theorem is, therefore, true for all angles that do not exceed two right angles. 39. **The sum of the squares of the sine and cosine of an** angle is equal to I. The right-angled triangle ACB (28) gives BCs-|-AC2 = AB2 ; substituting for the... | |
| George William Usill - Surveying - 1889 - 272 pages
...the sum of the squares of the chord of an arc, and of the chord of its supplement to a semicircle. 2. **The square of the radius is equal to the sum of the** squares of the sine and cosine. 3. The sum of the cosine and versed- sine is equal to the radius. 4.... | |
| Albert Johannsen - Optical mineralogy - 1914 - 649 pages
...T~+ cos / 21T/1 27T/2 , 2T/1 . 2lT/J\ + 2r1r. ^cos-j, • cos „, + sin „- • sin „, J • But **the sum of the squares of the sine and cosine of an** angle is equal to unity,1 and the sum of the product of the sines and cosines of two angles is equal... | |
| John Wesley Young, Albert John Schwartz - Geometry, Plane - 1915 - 223 pages
...cosine of its supplement, respectively, § 457, the same relation holds for obtuse angles. Hence : **The sum of the squares of the sine and cosine of an** (oblique) angle is equal to unity. 459. EXERCISES 1. Given A an acute angle and sin A = f ; find cos... | |
| Anthony Nicolaides - Mathematics - 1995 - 320 pages
...TRIGONOMETRIC FUNCTIONS AND THEIR APPLICATIONS I sin2 x + cos2 x = I ... (I) This expression states that **the sum of the squares of the sine and cosine of an** angle is identically equal to unity. 1dentically equal means that it is true for any value of л ,... | |
| Stan Gibilisco - Mathematics - 2010 - 412 pages
...less than 360° (2n rad). CHAPTER 11 Trigonometric Functions PYTHAGOREAN THEOREM FOR SINE AND COSINE **The sum of the squares of the sine and cosine of an** angle is always equal to 1 . The following formula holds: sin2 9 + cos2 9= 1 A NOTE ABOUT EXPONENTS... | |
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